Partial differential equations related to multivariate phase type distributions | Shuyuan Qin
| | Abstract | Phase-type distributions can be understood as the distributions of absorption times of certain Markov jump processes. Phase type distributions constitute a class of distributions on the nonnegative real axis. The concept can be expanded into higher dimensions, thus multivariate phase type distributions (MPH) are obtained. We could associate the total accumulated reward until absorption in a finite state with phase type distributions. Under this background V.G. Kulkarni introduced a new class of multivariate phase type distributions (denoted by MPH*). Usually it is difficult to compute this distribution directly. There are several computation techniques for the distributions in MPH*, of which we have a particular interest in the PDE method. Since it is not an easy task to solve the partial differential equations directly, we have introduced power series method to see the possibilities of obtaining the distributions or survival functions. Several concrete examples have shown that the recursive equations generated from the PDEs are valid.
Finally we use some numerical tests to confirm the feasibility of the PDE-Power series method to obtain the approximate survival functions of multivariate phase type distributed random variables. | | Type | Master's thesis [Academic thesis] | | Year | 2011 | | Publisher | Technical University of Denmark, DTU Informatics, E-mail: reception@imm.dtu.dk | | Address | Asmussens Alle, Building 305, DK-2800 Kgs. Lyngby, Denmark | | Series | IMM-M.Sc.-2011-85 | | Note | Supervised by Associate Professor Bo Friis Nielsen, bfn@imm.dtu.dk, DTU Informatics, and David Meisch | | Electronic version(s) | [pdf] | | Publication link | http://www.imm.dtu.dk/English.aspx | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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